VPN and WiFi sharing

I have a 2014 Mac mini connected to my LAN by ethernet. I've installed a VPN app, so all internet traffic from that mini goes through a private server. It works just fine with the VPN running.

So I had the idea to turn on internet sharing, so the mini would broadcast a WiFi channel that would then be routed through the VPN. The idea would be to allow me to connect to that WiFi with any other device--phone, laptop, tablet--and get the benefit of the VPN on the mini.

But when I tried it, none of the connected mobile devices could communicate through the system. They connect to the WiFi signal, but when you try to open a website you get a message that it can't connect to the server. If I turn the VPN off, then the mobile devices connect fine through the mini.

So there's some combination of settings between the internet sharing and the VPN app that are clogging it up. Any ideas?